Abstract
This paper shows, that Runge-Kutta-processes, also those with multiple nodes, having been extended in a certain way from symmetrical quadrature formulas satisfy the following condition: The method with step size −h is the inverse of the method with step size +h.
Zusammenfassung
Es wird gezeigt, daß Runge-Kutta-Methoden, auch solche mit mehrfachen Knoten, welche in einer gewissen Weise aus symmetrischen Quadraturformeln gewonnen wurden, folgendes erfüllen: Die Methode mit der Schrittweite −h ist die Inverse zur Methode mit Schrittweite +h.
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References
Butcher, J. C.: Implicit RK Processes. Math. Comp.18, 50–64 (1964).
Kastlunger, K., andG. Wanner: On Turan Type Implicit RK Methods. Computing9, 317–325 (1972).
Butcher, J. C.: An Algebraic Theory of Integration Processes. Math. Comp.26, 79–107 (1972).
Ehle, B.: On Padé Approximations to the Exponential Functions andA-stable Methods for the numerical solution of initial value problems. Thesis. Univ. of Waterloo. 1969.
Stetter, H. J.: Analysis of Discretization Methods for Ordinary Differential Equations. (Springer Tracts, Vol. 23). Berlin-Heidelberg-New York: Springer. 1973.
Stetter, H. J.: Symmetric two-step algorithms for ordinary differential equations. Computing5, 267–280 (1970).
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Wanner, G. Runge-Kutta-methods with expansion in even powers of h. Computing 11, 81–85 (1973). https://doi.org/10.1007/BF02239476
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DOI: https://doi.org/10.1007/BF02239476